TSTP Solution File: FLD040-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GrEaloO1ho true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:39:22 EDT 2023
% Result : Unsatisfiable 227.89s 34.02s
% Output : Refutation 227.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GrEaloO1ho true
% 0.13/0.31 % Computer : n016.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Sun Aug 27 23:51:29 EDT 2023
% 0.13/0.31 % CPUTime :
% 0.13/0.31 % Running portfolio for 300 s
% 0.13/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.32 % Number of cores: 8
% 0.13/0.32 % Python version: Python 3.6.8
% 0.13/0.32 % Running in FO mode
% 0.16/0.53 % Total configuration time : 435
% 0.16/0.53 % Estimated wc time : 1092
% 0.16/0.53 % Estimated cpu time (7 cpus) : 156.0
% 0.16/0.62 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.16/0.63 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.16/0.64 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.16/0.64 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.16/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.16/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.16/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 227.89/34.02 % Solved by fo/fo3_bce.sh.
% 227.89/34.02 % BCE start: 29
% 227.89/34.02 % BCE eliminated: 0
% 227.89/34.02 % PE start: 29
% 227.89/34.02 logic: neq
% 227.89/34.02 % PE eliminated: 0
% 227.89/34.02 % done 21902 iterations in 33.354s
% 227.89/34.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 227.89/34.02 % SZS output start Refutation
% 227.89/34.02 thf(sum_type, type, sum: $i > $i > $i > $o).
% 227.89/34.02 thf(a_type, type, a: $i).
% 227.89/34.02 thf(product_type, type, product: $i > $i > $i > $o).
% 227.89/34.02 thf(additive_identity_type, type, additive_identity: $i).
% 227.89/34.02 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 227.89/34.02 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 227.89/34.02 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 227.89/34.02 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 227.89/34.02 thf(defined_type, type, defined: $i > $o).
% 227.89/34.02 thf(existence_of_inverse_addition, axiom,
% 227.89/34.02 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 227.89/34.02 ( ~( defined @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl3, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 227.89/34.02 thf(existence_of_identity_addition, axiom,
% 227.89/34.02 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl2, plain,
% 227.89/34.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 227.89/34.02 thf(associativity_addition_1, axiom,
% 227.89/34.02 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 227.89/34.02 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 227.89/34.02 thf(zip_derived_cl0, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (sum @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 227.89/34.02 thf(zip_derived_cl38, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ X0 @ X2 @ X1)
% 227.89/34.02 | ~ (sum @ X0 @ X2 @ X3)
% 227.89/34.02 | (sum @ additive_identity @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl519, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X1 @ additive_identity)
% 227.89/34.02 | ~ (sum @ (additive_inverse @ X0) @ X0 @ X1)
% 227.89/34.02 | ~ (defined @ (additive_inverse @ X0)))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl38])).
% 227.89/34.02 thf(well_definedness_of_additive_inverse, axiom,
% 227.89/34.02 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl14, plain,
% 227.89/34.02 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 227.89/34.02 thf(zip_derived_cl16210, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (sum @ (additive_inverse @ X0) @ X0 @ X1)
% 227.89/34.02 | (sum @ additive_identity @ X1 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('clc', [status(thm)], [zip_derived_cl519, zip_derived_cl14])).
% 227.89/34.02 thf(well_definedness_of_multiplicative_identity, axiom,
% 227.89/34.02 (defined @ multiplicative_identity)).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(totality_of_order_relation, axiom,
% 227.89/34.02 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 227.89/34.02 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 227.89/34.02 thf(zip_derived_cl22, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (less_or_equal @ X0 @ X1)
% 227.89/34.02 | (less_or_equal @ X1 @ X0)
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | ~ (defined @ X1))),
% 227.89/34.02 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 227.89/34.02 thf(zip_derived_cl73, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (less_or_equal @ X0 @ multiplicative_identity)
% 227.89/34.02 | (less_or_equal @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl22])).
% 227.89/34.02 thf(zip_derived_cl1533, plain,
% 227.89/34.02 (( (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 227.89/34.02 | (less_or_equal @ multiplicative_identity @ multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl73])).
% 227.89/34.02 thf(zip_derived_cl1538, plain,
% 227.89/34.02 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl1533])).
% 227.89/34.02 thf(antisymmetry_of_order_relation, axiom,
% 227.89/34.02 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 227.89/34.02 ( ~( less_or_equal @ Y @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl20, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ X1)
% 227.89/34.02 | ~ (less_or_equal @ X0 @ X1)
% 227.89/34.02 | ~ (less_or_equal @ X1 @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 227.89/34.02 thf(zip_derived_cl2, plain,
% 227.89/34.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 227.89/34.02 thf(commutativity_addition, axiom,
% 227.89/34.02 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl39, plain,
% 227.89/34.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl39, plain,
% 227.89/34.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl39, plain,
% 227.89/34.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 227.89/34.02 thf(sum_3, conjecture,
% 227.89/34.02 (~( sum @
% 227.89/34.02 additive_identity @ additive_identity @ ( multiplicative_inverse @ a ) ))).
% 227.89/34.02 thf(zf_stmt_0, negated_conjecture,
% 227.89/34.02 (sum @
% 227.89/34.02 additive_identity @ additive_identity @ ( multiplicative_inverse @ a )),
% 227.89/34.02 inference('cnf.neg', [status(esa)], [sum_3])).
% 227.89/34.02 thf(zip_derived_cl28, plain,
% 227.89/34.02 ( (sum @ additive_identity @ additive_identity @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 227.89/34.02 thf(associativity_addition_2, axiom,
% 227.89/34.02 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 227.89/34.02 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 227.89/34.02 thf(zip_derived_cl1, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X3 @ X4 @ X0)
% 227.89/34.02 | ~ (sum @ X4 @ X1 @ X5)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_2])).
% 227.89/34.02 thf(zip_derived_cl51, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (sum @ additive_identity @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X2 @ X1)
% 227.89/34.02 | (sum @ (multiplicative_inverse @ a) @ X2 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 227.89/34.02 thf(zip_derived_cl272, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ additive_identity)
% 227.89/34.02 | (sum @ (multiplicative_inverse @ a) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl51])).
% 227.89/34.02 thf(well_definedness_of_additive_identity, axiom,
% 227.89/34.02 (defined @ additive_identity)).
% 227.89/34.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 227.89/34.02 thf(zip_derived_cl284, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ (multiplicative_inverse @ a) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl272, zip_derived_cl13])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl308, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | (sum @ X0 @ (multiplicative_inverse @ a) @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl317, plain,
% 227.89/34.02 ((~ (defined @ additive_identity)
% 227.89/34.02 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 227.89/34.02 additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl308])).
% 227.89/34.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 227.89/34.02 thf(zip_derived_cl325, plain,
% 227.89/34.02 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 227.89/34.02 additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl317, zip_derived_cl13])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl332, plain,
% 227.89/34.02 ( (sum @ (multiplicative_inverse @ a) @ additive_identity @
% 227.89/34.02 additive_identity)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl325, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl28, plain,
% 227.89/34.02 ( (sum @ additive_identity @ additive_identity @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 227.89/34.02 thf(zip_derived_cl0, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (sum @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 227.89/34.02 thf(zip_derived_cl29, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (sum @ (multiplicative_inverse @ a) @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X1 @ X2)
% 227.89/34.02 | (sum @ additive_identity @ X2 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl377, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl29])).
% 227.89/34.02 thf(zip_derived_cl409, plain,
% 227.89/34.02 ((~ (defined @ additive_identity)
% 227.89/34.02 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl377])).
% 227.89/34.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 227.89/34.02 thf(zip_derived_cl418, plain,
% 227.89/34.02 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl409, zip_derived_cl13])).
% 227.89/34.02 thf(zip_derived_cl0, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (sum @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 227.89/34.02 thf(zip_derived_cl422, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (sum @ additive_identity @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X1 @ X2)
% 227.89/34.02 | (sum @ additive_identity @ X2 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl418, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl1295, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X1 @ X0))),
% 227.89/34.02 inference('eq_fact', [status(thm)], [zip_derived_cl422])).
% 227.89/34.02 thf(zip_derived_cl1306, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (less_or_equal @ X0 @ X1)
% 227.89/34.02 | ~ (less_or_equal @ X1 @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl1295])).
% 227.89/34.02 thf(zip_derived_cl1576, plain,
% 227.89/34.02 (( (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)
% 227.89/34.02 | ~ (less_or_equal @ multiplicative_identity @ multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1538, zip_derived_cl1306])).
% 227.89/34.02 thf(zip_derived_cl1538, plain,
% 227.89/34.02 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl1533])).
% 227.89/34.02 thf(zip_derived_cl1578, plain,
% 227.89/34.02 ( (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl1576, zip_derived_cl1538])).
% 227.89/34.02 thf(zip_derived_cl3, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 227.89/34.02 thf(zip_derived_cl0, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (sum @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 227.89/34.02 thf(zip_derived_cl56, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X2 @ X1)
% 227.89/34.02 | ~ (sum @ X0 @ X2 @ X3)
% 227.89/34.02 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl1593, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (sum @ (additive_inverse @ X1) @ X0 @ multiplicative_identity)
% 227.89/34.02 | ~ (sum @ X1 @ multiplicative_identity @ X0)
% 227.89/34.02 | ~ (defined @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1578, zip_derived_cl56])).
% 227.89/34.02 thf(zip_derived_cl66286, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 additive_identity)
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ X0 @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('sup+', [status(thm)],
% 227.89/34.02 [zip_derived_cl16210, zip_derived_cl1593])).
% 227.89/34.02 thf(zip_derived_cl66300, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (sum @ X0 @ multiplicative_identity @ X0)
% 227.89/34.02 | (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl66286])).
% 227.89/34.02 thf(zip_derived_cl284, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ (multiplicative_inverse @ a) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl272, zip_derived_cl13])).
% 227.89/34.02 thf(zip_derived_cl325, plain,
% 227.89/34.02 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 227.89/34.02 additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl317, zip_derived_cl13])).
% 227.89/34.02 thf(zip_derived_cl1578, plain,
% 227.89/34.02 ( (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl1576, zip_derived_cl1538])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl1582, plain,
% 227.89/34.02 ( (sum @ multiplicative_identity @ additive_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1578, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl1, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X3 @ X4 @ X0)
% 227.89/34.02 | ~ (sum @ X4 @ X1 @ X5)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_2])).
% 227.89/34.02 thf(zip_derived_cl54, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (sum @ X2 @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ X1 @ X3 @ X1)
% 227.89/34.02 | (sum @ X0 @ X3 @ X0))),
% 227.89/34.02 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 227.89/34.02 thf(zip_derived_cl1609, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ multiplicative_identity @ X0 @ multiplicative_identity)
% 227.89/34.02 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1582, zip_derived_cl54])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl6009, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1609, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl6188, plain,
% 227.89/34.02 ( (sum @ (multiplicative_inverse @ a) @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl325, zip_derived_cl6009])).
% 227.89/34.02 thf(zip_derived_cl28, plain,
% 227.89/34.02 ( (sum @ additive_identity @ additive_identity @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 227.89/34.02 thf(zip_derived_cl39, plain,
% 227.89/34.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl29, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (sum @ (multiplicative_inverse @ a) @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X1 @ X2)
% 227.89/34.02 | (sum @ additive_identity @ X2 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl133, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ (multiplicative_inverse @ a))
% 227.89/34.02 | (sum @ additive_identity @ X0 @ (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl29])).
% 227.89/34.02 thf(not_sum_2, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 227.89/34.02 thf(zf_stmt_1, negated_conjecture,
% 227.89/34.02 (~( sum @ additive_identity @ a @ additive_identity )),
% 227.89/34.02 inference('cnf.neg', [status(esa)], [not_sum_2])).
% 227.89/34.02 thf(zip_derived_cl27, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ a @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 227.89/34.02 thf(well_definedness_of_multiplicative_inverse, axiom,
% 227.89/34.02 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 227.89/34.02 ( sum @ additive_identity @ X @ additive_identity ))).
% 227.89/34.02 thf(zip_derived_cl17, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (defined @ (multiplicative_inverse @ X0))
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_inverse])).
% 227.89/34.02 thf(zip_derived_cl45, plain,
% 227.89/34.02 ((~ (defined @ a) | (defined @ (multiplicative_inverse @ a)))),
% 227.89/34.02 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl17])).
% 227.89/34.02 thf(a_is_defined, axiom, (defined @ a)).
% 227.89/34.02 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 227.89/34.02 inference('cnf', [status(esa)], [a_is_defined])).
% 227.89/34.02 thf(zip_derived_cl46, plain, ( (defined @ (multiplicative_inverse @ a))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl26])).
% 227.89/34.02 thf(zip_derived_cl136, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl46])).
% 227.89/34.02 thf(zip_derived_cl144, plain,
% 227.89/34.02 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl136])).
% 227.89/34.02 thf(zip_derived_cl0, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (sum @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (sum @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 227.89/34.02 thf(zip_derived_cl149, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (sum @ (multiplicative_inverse @ a) @ X1 @ X0)
% 227.89/34.02 | ~ (sum @ (multiplicative_inverse @ a) @ X1 @ X2)
% 227.89/34.02 | (sum @ additive_identity @ X2 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl6308, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 227.89/34.02 | ~ (sum @ (multiplicative_inverse @ a) @ multiplicative_identity @
% 227.89/34.02 X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl6188, zip_derived_cl149])).
% 227.89/34.02 thf(zip_derived_cl8382, plain,
% 227.89/34.02 ((~ (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 additive_identity)
% 227.89/34.02 | (sum @ additive_identity @ additive_identity @
% 227.89/34.02 multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl6308])).
% 227.89/34.02 thf(different_identities, axiom,
% 227.89/34.02 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 227.89/34.02 thf(zip_derived_cl25, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [different_identities])).
% 227.89/34.02 thf(zip_derived_cl8387, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl8382, zip_derived_cl25])).
% 227.89/34.02 thf(zip_derived_cl67807, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0) | ~ (sum @ X0 @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('clc', [status(thm)], [zip_derived_cl66300, zip_derived_cl8387])).
% 227.89/34.02 thf(existence_of_identity_multiplication, axiom,
% 227.89/34.02 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl7, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 227.89/34.02 thf(zip_derived_cl7, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 227.89/34.02 thf(distributivity_1, axiom,
% 227.89/34.02 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 227.89/34.02 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 227.89/34.02 ( ~( product @ Y @ Z @ D ) ))).
% 227.89/34.02 thf(zip_derived_cl10, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X3 @ X4 @ X5)
% 227.89/34.02 | ~ (product @ X5 @ X6 @ X2)
% 227.89/34.02 | ~ (product @ X3 @ X6 @ X0)
% 227.89/34.02 | ~ (product @ X4 @ X6 @ X1))),
% 227.89/34.02 inference('cnf', [status(esa)], [distributivity_1])).
% 227.89/34.02 thf(zip_derived_cl163, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (product @ X2 @ X0 @ X1)
% 227.89/34.02 | ~ (product @ X4 @ X0 @ X3)
% 227.89/34.02 | ~ (sum @ X4 @ X2 @ multiplicative_identity)
% 227.89/34.02 | (sum @ X3 @ X1 @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl10])).
% 227.89/34.02 thf(zip_derived_cl4458, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ X1 @ X0 @ X0)
% 227.89/34.02 | ~ (sum @ X2 @ multiplicative_identity @ multiplicative_identity)
% 227.89/34.02 | ~ (product @ X2 @ X0 @ X1)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl163])).
% 227.89/34.02 thf(zip_derived_cl4463, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (product @ X2 @ X0 @ X1)
% 227.89/34.02 | ~ (sum @ X2 @ multiplicative_identity @ multiplicative_identity)
% 227.89/34.02 | (sum @ X1 @ X0 @ X0)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl4458])).
% 227.89/34.02 thf(zip_derived_cl1582, plain,
% 227.89/34.02 ( (sum @ multiplicative_identity @ additive_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1578, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl20, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ X1)
% 227.89/34.02 | ~ (less_or_equal @ X0 @ X1)
% 227.89/34.02 | ~ (less_or_equal @ X1 @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 227.89/34.02 thf(zip_derived_cl136, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl46])).
% 227.89/34.02 thf(zip_derived_cl142, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (less_or_equal @ X0 @ additive_identity)
% 227.89/34.02 | ~ (less_or_equal @ additive_identity @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ (multiplicative_inverse @ a)))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl136])).
% 227.89/34.02 thf(zip_derived_cl56, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ additive_identity @ X2 @ X1)
% 227.89/34.02 | ~ (sum @ X0 @ X2 @ X3)
% 227.89/34.02 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 227.89/34.02 thf(zip_derived_cl4166, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (less_or_equal @ additive_identity @ X0)
% 227.89/34.02 | ~ (less_or_equal @ X0 @ additive_identity)
% 227.89/34.02 | (sum @ (additive_inverse @ X2) @ X1 @ (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (sum @ X2 @ X0 @ X1)
% 227.89/34.02 | ~ (defined @ X2))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl56])).
% 227.89/34.02 thf(zip_derived_cl172210, plain,
% 227.89/34.02 ((~ (defined @ multiplicative_identity)
% 227.89/34.02 | (sum @ (additive_inverse @ multiplicative_identity) @
% 227.89/34.02 multiplicative_identity @ (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (less_or_equal @ additive_identity @ additive_identity)
% 227.89/34.02 | ~ (less_or_equal @ additive_identity @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl1582, zip_derived_cl4166])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 227.89/34.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 227.89/34.02 thf(zip_derived_cl22, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (less_or_equal @ X0 @ X1)
% 227.89/34.02 | (less_or_equal @ X1 @ X0)
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | ~ (defined @ X1))),
% 227.89/34.02 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 227.89/34.02 thf(zip_derived_cl71, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (less_or_equal @ X0 @ additive_identity)
% 227.89/34.02 | (less_or_equal @ additive_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl22])).
% 227.89/34.02 thf(zip_derived_cl1436, plain,
% 227.89/34.02 (( (less_or_equal @ additive_identity @ additive_identity)
% 227.89/34.02 | (less_or_equal @ additive_identity @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl71])).
% 227.89/34.02 thf(zip_derived_cl1443, plain,
% 227.89/34.02 ( (less_or_equal @ additive_identity @ additive_identity)),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl1436])).
% 227.89/34.02 thf(zip_derived_cl1443, plain,
% 227.89/34.02 ( (less_or_equal @ additive_identity @ additive_identity)),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl1436])).
% 227.89/34.02 thf(zip_derived_cl172529, plain,
% 227.89/34.02 ( (sum @ (additive_inverse @ multiplicative_identity) @
% 227.89/34.02 multiplicative_identity @ (multiplicative_inverse @ a))),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl172210, zip_derived_cl16, zip_derived_cl1443,
% 227.89/34.02 zip_derived_cl1443])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl196268, plain,
% 227.89/34.02 ( (sum @ multiplicative_identity @
% 227.89/34.02 (additive_inverse @ multiplicative_identity) @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl172529, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl7, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 227.89/34.02 thf(commutativity_multiplication, axiom,
% 227.89/34.02 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 227.89/34.02 thf(zip_derived_cl9, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 227.89/34.02 thf(zip_derived_cl55, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 227.89/34.02 thf(zip_derived_cl3, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl58, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 227.89/34.02 thf(distributivity_2, axiom,
% 227.89/34.02 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 227.89/34.02 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 227.89/34.02 ( ~( sum @ C @ D @ B ) ))).
% 227.89/34.02 thf(zip_derived_cl11, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (sum @ X3 @ X4 @ X0)
% 227.89/34.02 | ~ (product @ X3 @ X1 @ X5)
% 227.89/34.02 | ~ (product @ X4 @ X1 @ X6)
% 227.89/34.02 | ~ (sum @ X5 @ X6 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [distributivity_2])).
% 227.89/34.02 thf(zip_derived_cl203, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ X3 @ X2 @ X1)
% 227.89/34.02 | ~ (product @ (additive_inverse @ X0) @ X4 @ X2)
% 227.89/34.02 | ~ (product @ X0 @ X4 @ X3)
% 227.89/34.02 | (product @ additive_identity @ X4 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl11])).
% 227.89/34.02 thf(zip_derived_cl5692, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (defined @ (additive_inverse @ X0))
% 227.89/34.02 | (product @ additive_identity @ multiplicative_identity @ X1)
% 227.89/34.02 | ~ (product @ X0 @ multiplicative_identity @ X2)
% 227.89/34.02 | ~ (sum @ X2 @ (additive_inverse @ X0) @ X1)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl203])).
% 227.89/34.02 thf(zip_derived_cl14, plain,
% 227.89/34.02 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 227.89/34.02 thf(zip_derived_cl245866, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (sum @ X2 @ (additive_inverse @ X0) @ X1)
% 227.89/34.02 | ~ (product @ X0 @ multiplicative_identity @ X2)
% 227.89/34.02 | (product @ additive_identity @ multiplicative_identity @ X1))),
% 227.89/34.02 inference('clc', [status(thm)], [zip_derived_cl5692, zip_derived_cl14])).
% 227.89/34.02 thf(zip_derived_cl245951, plain,
% 227.89/34.02 (( (product @ additive_identity @ multiplicative_identity @
% 227.89/34.02 (multiplicative_inverse @ a))
% 227.89/34.02 | ~ (product @ multiplicative_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)
% 227.89/34.02 | ~ (defined @ multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)],
% 227.89/34.02 [zip_derived_cl196268, zip_derived_cl245866])).
% 227.89/34.02 thf(zip_derived_cl55, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 227.89/34.02 thf(existence_of_inverse_multiplication, axiom,
% 227.89/34.02 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 227.89/34.02 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 227.89/34.02 thf(zip_derived_cl8, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 227.89/34.02 multiplicative_identity)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 227.89/34.02 thf(zip_derived_cl7, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 227.89/34.02 thf(associativity_multiplication_1, axiom,
% 227.89/34.02 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 227.89/34.02 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 227.89/34.02 thf(zip_derived_cl5, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (product @ X0 @ X3 @ X4)
% 227.89/34.02 | ~ (product @ X3 @ X5 @ X1)
% 227.89/34.02 | ~ (product @ X4 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 227.89/34.02 thf(zip_derived_cl65, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (product @ X0 @ X2 @ X1)
% 227.89/34.02 | ~ (product @ X0 @ X2 @ X3)
% 227.89/34.02 | (product @ multiplicative_identity @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 227.89/34.02 thf(zip_derived_cl1273, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | (product @ multiplicative_identity @ X1 @ multiplicative_identity)
% 227.89/34.02 | ~ (product @ (multiplicative_inverse @ X0) @ X0 @ X1)
% 227.89/34.02 | ~ (defined @ (multiplicative_inverse @ X0)))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl65])).
% 227.89/34.02 thf(zip_derived_cl17, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (defined @ (multiplicative_inverse @ X0))
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_inverse])).
% 227.89/34.02 thf(zip_derived_cl52725, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (product @ (multiplicative_inverse @ X0) @ X0 @ X1)
% 227.89/34.02 | (product @ multiplicative_identity @ X1 @ multiplicative_identity)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('clc', [status(thm)], [zip_derived_cl1273, zip_derived_cl17])).
% 227.89/34.02 thf(zip_derived_cl52732, plain,
% 227.89/34.02 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 227.89/34.02 | ~ (defined @ multiplicative_identity)
% 227.89/34.02 | (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 additive_identity)
% 227.89/34.02 | (product @ multiplicative_identity @
% 227.89/34.02 (multiplicative_inverse @ multiplicative_identity) @
% 227.89/34.02 multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl52725])).
% 227.89/34.02 thf(zip_derived_cl17, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (defined @ (multiplicative_inverse @ X0))
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_inverse])).
% 227.89/34.02 thf(zip_derived_cl8387, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl8382, zip_derived_cl25])).
% 227.89/34.02 thf(zip_derived_cl8396, plain,
% 227.89/34.02 ((~ (defined @ multiplicative_identity)
% 227.89/34.02 | (defined @ (multiplicative_inverse @ multiplicative_identity)))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl8387])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl8399, plain,
% 227.89/34.02 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl8396, zip_derived_cl16])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl8387, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl8382, zip_derived_cl25])).
% 227.89/34.02 thf(zip_derived_cl52736, plain,
% 227.89/34.02 ( (product @ multiplicative_identity @
% 227.89/34.02 (multiplicative_inverse @ multiplicative_identity) @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl52732, zip_derived_cl8399, zip_derived_cl16,
% 227.89/34.02 zip_derived_cl8387])).
% 227.89/34.02 thf(zip_derived_cl65, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (product @ X0 @ X2 @ X1)
% 227.89/34.02 | ~ (product @ X0 @ X2 @ X3)
% 227.89/34.02 | (product @ multiplicative_identity @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 227.89/34.02 thf(zip_derived_cl1274, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (product @ multiplicative_identity @ X0 @ X0)
% 227.89/34.02 | ~ (product @ X2 @ X1 @ X0)
% 227.89/34.02 | ~ (defined @ X2))),
% 227.89/34.02 inference('eq_fact', [status(thm)], [zip_derived_cl65])).
% 227.89/34.02 thf(zip_derived_cl53411, plain,
% 227.89/34.02 ((~ (defined @ multiplicative_identity)
% 227.89/34.02 | (product @ multiplicative_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)],
% 227.89/34.02 [zip_derived_cl52736, zip_derived_cl1274])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl53425, plain,
% 227.89/34.02 ( (product @ multiplicative_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)], [zip_derived_cl53411, zip_derived_cl16])).
% 227.89/34.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 227.89/34.02 inference('cnf', [status(esa)],
% 227.89/34.02 [well_definedness_of_multiplicative_identity])).
% 227.89/34.02 thf(zip_derived_cl246094, plain,
% 227.89/34.02 ( (product @ additive_identity @ multiplicative_identity @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl245951, zip_derived_cl53425, zip_derived_cl16])).
% 227.89/34.02 thf(zip_derived_cl9, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 227.89/34.02 thf(zip_derived_cl246985, plain,
% 227.89/34.02 ( (product @ multiplicative_identity @ additive_identity @
% 227.89/34.02 (multiplicative_inverse @ a))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl246094, zip_derived_cl9])).
% 227.89/34.02 thf(zip_derived_cl8, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 227.89/34.02 multiplicative_identity)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 227.89/34.02 thf(zip_derived_cl9, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 227.89/34.02 thf(zip_derived_cl130, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 227.89/34.02 multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 227.89/34.02 thf(zip_derived_cl55, plain,
% 227.89/34.02 (![X0 : $i]:
% 227.89/34.02 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 227.89/34.02 thf(associativity_multiplication_2, axiom,
% 227.89/34.02 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 227.89/34.02 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 227.89/34.02 thf(zip_derived_cl6, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2)
% 227.89/34.02 | ~ (product @ X3 @ X4 @ X0)
% 227.89/34.02 | ~ (product @ X4 @ X1 @ X5)
% 227.89/34.02 | ~ (product @ X3 @ X5 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 227.89/34.02 thf(zip_derived_cl115, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 227.89/34.02 (~ (defined @ X0)
% 227.89/34.02 | ~ (product @ X0 @ X2 @ X1)
% 227.89/34.02 | ~ (product @ multiplicative_identity @ X3 @ X2)
% 227.89/34.02 | (product @ X0 @ X3 @ X1))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl6])).
% 227.89/34.02 thf(zip_derived_cl3665, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 ( (sum @ additive_identity @ X0 @ additive_identity)
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | (product @ X0 @ X1 @ multiplicative_identity)
% 227.89/34.02 | ~ (product @ multiplicative_identity @ X1 @
% 227.89/34.02 (multiplicative_inverse @ X0))
% 227.89/34.02 | ~ (defined @ X0))),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl115])).
% 227.89/34.02 thf(zip_derived_cl3674, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i]:
% 227.89/34.02 (~ (product @ multiplicative_identity @ X1 @
% 227.89/34.02 (multiplicative_inverse @ X0))
% 227.89/34.02 | (product @ X0 @ X1 @ multiplicative_identity)
% 227.89/34.02 | ~ (defined @ X0)
% 227.89/34.02 | (sum @ additive_identity @ X0 @ additive_identity))),
% 227.89/34.02 inference('simplify', [status(thm)], [zip_derived_cl3665])).
% 227.89/34.02 thf(zip_derived_cl247823, plain,
% 227.89/34.02 (( (sum @ additive_identity @ a @ additive_identity)
% 227.89/34.02 | ~ (defined @ a)
% 227.89/34.02 | (product @ a @ additive_identity @ multiplicative_identity))),
% 227.89/34.02 inference('sup-', [status(thm)],
% 227.89/34.02 [zip_derived_cl246985, zip_derived_cl3674])).
% 227.89/34.02 thf(zip_derived_cl27, plain,
% 227.89/34.02 (~ (sum @ additive_identity @ a @ additive_identity)),
% 227.89/34.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 227.89/34.02 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 227.89/34.02 inference('cnf', [status(esa)], [a_is_defined])).
% 227.89/34.02 thf(zip_derived_cl247875, plain,
% 227.89/34.02 ( (product @ a @ additive_identity @ multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl247823, zip_derived_cl27, zip_derived_cl26])).
% 227.89/34.02 thf(zip_derived_cl9, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 227.89/34.02 thf(zip_derived_cl247880, plain,
% 227.89/34.02 ( (product @ additive_identity @ a @ multiplicative_identity)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl247875, zip_derived_cl9])).
% 227.89/34.02 thf(zip_derived_cl248006, plain,
% 227.89/34.02 ((~ (defined @ a)
% 227.89/34.02 | (sum @ multiplicative_identity @ a @ a)
% 227.89/34.02 | ~ (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity))),
% 227.89/34.02 inference('sup+', [status(thm)],
% 227.89/34.02 [zip_derived_cl4463, zip_derived_cl247880])).
% 227.89/34.02 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 227.89/34.02 inference('cnf', [status(esa)], [a_is_defined])).
% 227.89/34.02 thf(zip_derived_cl1578, plain,
% 227.89/34.02 ( (sum @ additive_identity @ multiplicative_identity @
% 227.89/34.02 multiplicative_identity)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl1576, zip_derived_cl1538])).
% 227.89/34.02 thf(zip_derived_cl248017, plain, ( (sum @ multiplicative_identity @ a @ a)),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl248006, zip_derived_cl26, zip_derived_cl1578])).
% 227.89/34.02 thf(zip_derived_cl4, plain,
% 227.89/34.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 227.89/34.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 227.89/34.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 227.89/34.02 thf(zip_derived_cl248055, plain, ( (sum @ a @ multiplicative_identity @ a)),
% 227.89/34.02 inference('sup-', [status(thm)], [zip_derived_cl248017, zip_derived_cl4])).
% 227.89/34.02 thf(zip_derived_cl248416, plain, (~ (defined @ a)),
% 227.89/34.02 inference('sup+', [status(thm)],
% 227.89/34.02 [zip_derived_cl67807, zip_derived_cl248055])).
% 227.89/34.02 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 227.89/34.02 inference('cnf', [status(esa)], [a_is_defined])).
% 227.89/34.02 thf(zip_derived_cl248431, plain, ($false),
% 227.89/34.02 inference('demod', [status(thm)],
% 227.89/34.02 [zip_derived_cl248416, zip_derived_cl26])).
% 227.89/34.02
% 227.89/34.02 % SZS output end Refutation
% 227.89/34.02
% 227.89/34.02
% 227.89/34.02 % Terminating...
% 228.64/34.13 % Runner terminated.
% 228.64/34.14 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------